Second-order Nonlinear Multi-agent Systems Research Articles

Fully Distributed Event-Triggered Consensus for a Class of Second-Order Nonlinear Multi-agent Systems

Fully Distributed Event-Triggered Consensus for a Class of Second-Order Nonlinear Multi-agent Systems

Event-triggered H-infinity finite-time consensus control for nonlinear second-order multi-agent systems with disturbances

The study considers the problem of finite-time event-triggered H-infinity consensus for second-order multi-agent systems (MASs) with intrinsic nonlinear dynamics and external bounded disturbances. Based on the designed triggering function, a distributed event-triggered control strategy is presented on the basis of the designed triggering function to ensure consensus in the system, which effectively reduces the data transmission. Then, sufficient conditions for the finite-time consensus with H-infinity performance level of the resulting event-triggered MAS are derived by utilizing the Lyapunov function and finite-time stability theory. Furthermore, Zeno behavior is proven to be excluded under the proposed event-triggered scheme. Finally, the validity of the proposed results is verified by numerical simulation.

Network-based deployment of nonlinear multi agents over open curves: A PDE approach

Deployment of the first-order and second-order nonlinear multi agent systems over desired open (and, as a particular case, closed) smooth curves in 2D or 3D space is considered. The considered nonlinearities are globally Lipschitz. We assume that the agents have access to the local information of the desired curve and to their positions with respect to their closest neighbors (as well as to their velocities for the second-order systems), whereas in addition a leader agent is able to measure its absolute position. We assume that a small number of leaders (distributed in the spatial domain) transmit their measurements to other agents through a communication network. We take into account the following network imperfections: variable sampling, transmission delay and quantization. We propose a static output-feedback controller and model the resulting closed-loop system as a disturbed (due to quantization) nonlinear heat equation (for the first-order systems) or damped wave equation (for the second-order systems) with delayed point state measurements, where the state is the relative position of the agents with respect to the desired curve. In order to cope with the open curve we consider Neumann boundary conditions that ensure mobility of the boundary agents. We derive linear matrix inequalities (LMIs) that guarantee the input-to-state stability (ISS) of the system. The advantage of our approach is in the simplicity of the control law and the conditions. Numerical examples illustrate the efficiency of the method.

Event-Triggered Adaptive Fault-Tolerant Pinning Control for Cluster Consensus of Heterogeneous Nonlinear Multi-Agent Systems Under Aperiodic DoS Attacks

This paper presents an event-triggered cluster consensus scheme for heterogeneous nonlinear second-order multi-agent systems (MASs) subject to cyber attacks (i.e., aperiodic denial-of-service (DoS) attacks), actuator faults and integral quadratic constraints (IQCs) under directed communication topology containing a directed spanning tree. Based on local communication, an event-triggered adaptive fault-tolerant pinning control scheme is designed to achieve cluster consensus under simultaneous cyber attacks and actuator faults. The proposed control scheme does not require the communication topology to satisfy the in-degree balance between different clusters. Furthermore, the fault-tolerant control part only needs to estimate one parameter for each agent. Instead of requiring continuous information on its neighbors to determine the trigger instants as in the previous literature, an event-triggered mechanism that does not require periodic sampling of neighbors’ information is developed to save network resources, and the Zeno behavior is excluded. Finally, a simulation example confirms the effectiveness and superiority of the proposed control scheme.

Distributed event-triggered adaptive control for second-order nonlinear uncertain multi-agent systems

In this paper, the event-triggered consensus control problem for nonlinear uncertain multi-agent systems subject to unknown parameters and external disturbances is considered. The dynamics of subsystems are second-order with similar structures, and the nodes are connected by undirected graphs. The event-triggered mechanisms are not only utilized in the transmission of information from the controllers to the actuators, and from the sensors to the controllers within each agent, but also in the communication between agents. Based on the adaptive backstepping method, extra estimators are introduced to handle the unknown parameters, and the measurement errors that occur during the event-triggered communication are well handled by designing compensating terms for the control signals. The presented distributed event-triggered adaptive control laws can guarantee the boundness of the consensus tracking errors and the Zeno behavior is avoided. Meanwhile, the update frequency of the controllers and the load of communication burden are vastly reduced. The obtained control protocol is further applied to a multi-input multi-output second-order nonlinear multi-agent system, and the simulation results show the effectiveness and advantages of our proposed method.

Event-triggered consensus control of second-order nonlinear multi-agent systems under denial-of-service attacks

This paper investigates the event-triggered consensus problem of second-order nonlinear multi-agent systems subject to denial-of-service (DoS) attacks, which make the communication network unable to provide normal services. Considering a general class of DoS attack with limited duration, a novel distributed event-triggered consensus protocol accompanied with first-order hold is adopted to guarantee the globally bounded consensus convergence under directed network topology. Based on the linear matrix inequality approach and Lyapunov stability method, consensus converging properties are analysed and sufficient criteria are obtained. Furthermore, Zeno-free triggering of our proposed protocol is demonstrated. Finally, a numerical simulation is given to show the effectiveness of our theoretical results.

Leader-following Formation Control of Second-order Nonlinear Systems with Time-varying Communication Delay

In this paper, time-varying formation tracking problem for second-order nonlinear multi-agent systems with time-varying communication delays has been investigated, where the followers maintain a predefined time-varying formation while tracking the moving leader. Based on a distributed observer, a formation tracking protocol with time-varying delay is developed using the relative neighboring information. By constructing the Lyapunov-Krasovskii (L-K) function, sufficient conditions have been obtained to guarantee the stability of time-varying formation tracking. In addition, the unknown gain matrix in the proposed protocol is computed out through the technique of variable substitution. Numerical simulation results are presented to validate the effectiveness of our theoretical analysis.

Neural-network-based formation control with collision, obstacle avoidance and connectivity maintenance for a class of second-order nonlinear multi-agent systems

In this paper, a formation control strategy with collision, obstacle avoidance and connectivity maintenance is developed for a class of second-order nonlinear multi-agent systems under external disturbances. Firstly, in order to handle the nonlinear dynamics of the multi-agent systems and the unknown disturbances in the environment, neural network (NN) techniques are employed in the proposed control strategy. Then, the distributed formation controller with collision, obstacle avoidance is designed by combining artificial potential field (APF) methods and leader–follower formation methods. Secondly, due to the collision or obstacle avoidance terms within the formation controller may result in large separation distance among agents and each agent’s communication distance is limited by its hardware, the collision or obstacle avoidance terms increase the chance of losing connectivity between agents. In order to guarantee the connectivity of the formation, the connectivity maintenance controller is designed with taking the communication topology into account. Based on Lyapunov stability theory, it is proved that the stability of the closed-loop multi-agent systems can be guaranteed. Finally, the simulation results verify the effectiveness of the proposed approach.

Multi-Group Formation Tracking Control for Second-Order Nonlinear Multi-Agent Systems Using Adaptive Neural Networks

Multi-Group Formation Tracking Control for Second-Order Nonlinear Multi-Agent Systems Using Adaptive Neural Networks

Fully Distributed Containment Control for Second-Order Nonlinear Multi-Agent Systems With External Disturbances

Fully Distributed Containment Control for Second-Order Nonlinear Multi-Agent Systems With External Disturbances

Distributed cooperative control of autonomous multi-agent UAV systems using smooth control

This paper addresses the cooperative control problem of multiple unmanned aerial vehicles (multi-UAV) systems. First, a new distributed consensus algorithm for second-order nonlinear multi-agent systems (MAS) is formulated under the leader-following approach. The algorithm provides smooth input signals to the agents' control channels, which avoids the chattering effect generated by the conventional sliding mode-based control protocols. Second, a new formation control scheme is developed by integrating smooth distributed consensus control protocols into the geometric pattern model to achieve three-dimensional formation tracking. The Lyapunov theory is used to prove the stability and convergence of both distributed consensus and formation controllers. The effectiveness of the proposed algorithms is demonstrated through simulation results.

Adaptive Event-Triggered Consensus Control of a Class of Second-Order Nonlinear Multiagent Systems.

This paper addresses an adaptive event-triggered consensus control problem for a class of second-order nonlinear multiagent systems (MASs) in an undirected communication topology. A novel adaptive distributed event-triggered consensus control scheme is presented for the MAS with unknown functions based on the definition of an auxiliary state, and the coefficient of the triggered function can be regulated adaptively with dependence on the auxiliary state error to ensure not only the control performance but also the efficiency of the network interactions. Furthermore, two self-triggered algorithms are developed for two cases, known functions and unknown ones, by the current state and information at the previous event time instant instead of the requirement for continuous monitoring auxiliary state errors. In theory, the stability of the resulting closed-loop system is rigorously investigated, and it is proven that all signals in the closed-loop system are bounded and the Zeno behavior is ruled out. Finally, two simulation examples, both real-time and numerical ones, are provided to verify the theoretical claims.

Prescribed-time leader-following consensus for stochastic second-order multi-agent systems subject to actuator failures via sliding mode control strategy

Two control protocols based on the sliding mode control scheme are proposed to solve the prescribed-time leader-following consensus problem for second-order nonlinear multi-agent systems with actuator failures and stochastic noises under directed topology. First, a discontinuous controller protocol is proposed when the parameters related to the actuator failures can be acquired in advance. The controller can drive the system trajectories to reach the sliding manifold before a predefined time, and then ensure that the leader-following consensus is achieved in predefined time also. The upper bound of the reaching time and the upper bound of the setting time do not depend on initial conditions and system parameters, and can be arbitrarily specified offline. Next, when the prior knowledge of the actuator faults and nonlinearities cannot be obtained, a continuous control protocol is proposed, which can adaptively adjust the control gains to compensate for these unknown uncertainties. We theoretically prove that the prescribed-time leader-following consensus in mean square can be achieved under the designed control schemes. Finally, several examples are presented to illustrate the effectiveness of the proposed solutions.

Distributed consensus tracking control of second‐order non‐linear multi‐agent systems with unmodelled dynamics

In this study, the consensus tracking control problem is considered for a class of second-order non-linear multi-agent systems with unmodelled dynamics. Radial basis function neural networks are introduced to approximate the unknown non-linearities and a dynamic signal is utilised to deal with the unmodelled dynamics. Meanwhile, appropriate Lyapunov functions are constructed and a new distributed adaptive control protocol is designed to guarantee that all the tracking error signals in the considered multi-agent systems are ultimately bounded, under which the distributed tracking consensus is reached for all undirected connected communication graphs. Finally, two demonstrative examples are given to illustrate the validity of the designed protocols.

Adaptive non‐singular fast terminal sliding mode control for multi‐agent systems with unknown non‐linear dynamics

This study considers the finite time consensus tracking problems for second-order non-linear multi-agent system with the unknown dynamics. Firstly, the radial basis function neural networks are utilised to approximate the lumped unknown dynamic model. And then, to achieve the finite-time consensus tracking, a distributed non-singular fast terminal sliding mode control strategy is designed which can speed up the convergence of the multi-agent system. Moreover, the consistency under the proposed control strategy is theoretically analysed and the upper bound of setting time is explicitly obtained. Finally, two simulation examples are provided.

Completely distributed neuro-learning consensus with position constraints and partially unknown control directions

In this paper, we propose a new neural network-based iterative learning leader-less consensus control algorithm for the second-order uncertain time-varying nonlinear multi-agent systems, where the position of each agent is constrained in an open interval which can be pre-selected and the control direction can be non-identical and partially unknown. With the help of a novel barrier composite energy function and multiple piece-wise Nussbaum functions, the designed completely distributed learning protocols can make the positions and velocities of the agents achieve the exact consensus on a finite time interval as the iteration number increases to infinity. Meanwhile, the position trajectories of the agents at each iteration do not exceed the constraints bounds. Besides, to testify the feasibility and utility of the presented algorithm, two simulation examples are given in the end.

Consensus of Heterogeneous Second-Order Nonlinear Uncertain Multiagent Systems Under Switching Networks

The consensus problem of heterogeneous second-order nonlinear uncertain multiagent systems under switching networks is addressed by a distributed control approach. The network communication of all systems is subject to arbitrarily bounded and nonuniform time-varying delays. Based on the internal model principle, a nonlinear distributed dynamic controller is developed to solve the problem. By means of Lyapunov analysis, consensus of heterogeneous second-order nonlinear multiagent systems is achieved in the presence of system uncertainties, disturbances, and uniformly connected topologies as well as arbitrarily bounded and nonuniform time-varying communication delays.

Finite-time consensus of second-order nonlinear multi-agent systems with impulsive effects

This paper addresses finite-time consensus of second-order nonlinear multi-agent systems with impulsive effects. A control protocol contains neighborhood and self state feedback without sign function is proposed for finite-time consensus. By employing Lyapunov stability theory, a new less conservative estimation of energy function is obtained, by solving which, it gets both finite-time consensus and exponential consensus criteria with or without impulsive effects. Moreover, three impulsive types: stability, divergence and no effects, are divided based on strengths of impulse and controller. Examples are provided to demonstrate the correctness of theoretical results and the effectiveness of the finite-time protocol.

Global Adaptive Leader-Following Consensus for Second-Order Nonlinear Multiagent Systems With Switching Topologies

In this note, the leader-following consensus problem is considered for a class of second-order nonlinear multiagent systems, where the communication topology is switching. In view of that the Lipschitz constants of nonlinear terms are unknown, adaptive control strategy is adopted. Using the back-stepping technique, a new adaptive protocol is proposed. It is noted that the global information, including the eigenvalues of Laplacian matrix, is not used in the protocol design. It is proven that the practical leader-following consensus can be reached by the given control scheme. Finally, we present a numerical example to show the effectiveness of the proposed protocol.

Consensus and $H_{\infty }$ Consensus of Nonlinear Second-Order Multi-Agent Systems

This paper investigates the consensus problem for a class of nonlinear second-order multi-agent system with and without external disturbances. First, by making use of some inequality techniques and the designed state feedback controller, a consensus criterion is presented for the multi-agent system. In addition, an adaptive control scheme is also developed to ensure the consensus of the multi-agent system. Moreover, we further discuss the $H_{\infty }$ consensus problem for the multi-agent system, and some $H_{\infty }$ consensus criteria are acquired by using the designed state feedback controller and adaptive state feedback controller. Finally, we propose two numerical examples to verify the effectiveness of these obtained results.